Sure. Sorry about the quality, it was taken on my tablet, it's the only camera I have without an IR filter. I'm showing you the right side there, but the left side is the same. The brighter blue light is the mode light, the dimmer two are the outer IR leds.

your Dolphinbar appears to be defective, all 5 IR LEDs on each side should be clearly lit when viewed with a digital camera. Mine Dolphinbar is defective as well, it simply refuses to pair with any remote, I made a thread about it here recently.

Well, recently I had a similar problem with the right side of my Dolphin. Did a little investigation and one of the IR LEDs was burnt but since they're connected in series, the three LEDs won't light. I replaced the IR LED that was burnt and everything worked normally again. However, in your case, since both sides are showing the same problem, I suggest inspecting the voltage regulators too...

Well, at least mine I would say that it was my cause: took a little trip and someone left my Dolphin Bar plugged in computer at least 3 days, without any interruption. When I arrived, the bar was too hot, burning, and one side showed this problem. However, after replacing the burnt LED, it's working like it was when I bought...

Could anybody tell me in layman's terms how I would go about testing where the fault is? I have some spare LEDs that I could switch out, but how could I tell which one (if not all) of them is faulty, or if it is the voltage regulator as Jhonn has suggested?

I have a multimeter, but I don't even know what a voltage regulator looks like...

Well, I didn't found photos of the Dolphin Bar board and I'm away from mine now, but try checking the voltage in the LED contacts like this mockup I tried to draw here:

Code:

. v + + +
| | | |'''| |'''| | | |
[*] [ ] [ ] [ ] [*]

The "[ ]" are the LEDs, "| |" are the LED connectors. Plug one test point of your multimeter in the v and plug the another test point in every + (test one by one). They should read approximately 1.5V~4V in your multimeter, depending of the test point. You'll eventually find one + where there's no reading (0V), indicating the LED before that + is the one that burned.
About voltage regulator, forget that, if it have burned, none of the LEDs would light up and from what you said, the first and last LED in each side are working...